Example 4.3.1. Let \(\underline{X}=(X_1,X_2)\)  be a random variables with Mckay's bivariate gamma pdf (see Chapter 48 of [1]}) \(f_{\underline{\theta }}(x_1,x_2)=\frac{1}{\theta _1\theta _2}f\left(\frac{x_1}{\theta _1},\frac{x_2}{\theta _2}\right),\; (x_1,x_2)\in \Re ^2,\) 
where
\(f(z_1,z_2)= {\left\lbrace \begin{array}{ll}\frac{(z_2-z_1)^{\alpha _2-1}\,z_1^{\alpha _1-1}\,e^{-z_2}}{\Gamma \alpha _1 \Gamma \alpha _2},\; \; &0<z_1<z_2<\infty \\0,\qquad \qquad \qquad \qquad &\text{ otherwise}\end{array}\right.} , \) 
